Finite Math Examples

$7 x + y = 7$ , $y = - 3 x + 3$

Step 1

Replace all occurrences of $y$ with $- 3 x + 3$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $7 x + y = 7$ with $- 3 x + 3$ .

$7 x - 3 x + 3 = 7$

$y = - 3 x + 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $7 x - 3 x + 3$ .

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Step 1.2.1.1

Remove parentheses.

$7 x - 3 x + 3 = 7$

$y = - 3 x + 3$

Step 1.2.1.2

Subtract $3 x$ from $7 x$ .

$4 x + 3 = 7$

$y = - 3 x + 3$

$4 x + 3 = 7$

$y = - 3 x + 3$

$4 x + 3 = 7$

$y = - 3 x + 3$

$4 x + 3 = 7$

$y = - 3 x + 3$

Step 2

Solve for $x$ in $4 x + 3 = 7$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1.1

Subtract $3$ from both sides of the equation.

$4 x = 7 - 3$

$y = - 3 x + 3$

Step 2.1.2

Subtract $3$ from $7$ .

$4 x = 4$

$y = - 3 x + 3$

$4 x = 4$

$y = - 3 x + 3$

Step 2.2

Divide each term in $4 x = 4$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

$y = - 3 x + 3$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

$y = - 3 x + 3$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{4}$

$y = - 3 x + 3$

$x = \frac{4}{4}$

$y = - 3 x + 3$

$x = \frac{4}{4}$

$y = - 3 x + 3$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $4$ by $4$ .

$x = 1$

$y = - 3 x + 3$

$x = 1$

$y = - 3 x + 3$

$x = 1$

$y = - 3 x + 3$

$x = 1$

$y = - 3 x + 3$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = - 3 x + 3$ with $1$ .

$y = - 3 \cdot 1 + 3$

$x = 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 3 \cdot 1 + 3$ .

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Step 3.2.1.1

Multiply $- 3$ by $1$ .

$y = - 3 + 3$

$x = 1$

Step 3.2.1.2

Add $- 3$ and $3$ .

$y = 0$

$x = 1$

$y = 0$

$x = 1$

$y = 0$

$x = 1$

$y = 0$

$x = 1$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 0)$

Equation Form:

$x = 1, y = 0$

Step 6